I agree - plenty to do. We did not get to everything, even with 2 days. There are opportunities to wander around and explore that an extra day would really allow you to enjoy, like the indoor flea market near the hotel that includes some wonderful local artisans who were fascinating to talk with. I also agree about at least one pre day, both for the jet lag and bc the shopping is wonderful, especially for outdoor gear that can be less available in the states, which you might want for the adventure.
I know people keep saying how expensive Iceland is, but I have to say I did not find prices out of line with any other resort type setting. Maybe because I live in a tourist town, I’m used to meals and activities being pricey. (Good meals for the 3 of us in the $150-175 range) I actually thought some of the coats, backpacks, etc in the nice outdoor stores were very competitive to what I’ve seen at home. Drinks were more expensive, but so are drinks at WDW.
Anyway, enjoy your extra days!